The Mackey Machine for Crossed Products by Regular Groupoids. II

Geoff Goehle

The Mackey Machine for Crossed Products by Regular Groupoids. II

Operator Algebras 2009-10-07 v2

Authors: Geoff Goehle

Abstract

We prove that given a regular groupoid $G$ whose isotropy subgroupoid $S$ has a Haar system, along with a dynamical system $(A,G,\alpha)$ , there is an action of $G$ on the spectrum of $A\rtimes S$ such that the spectrum of $A\rtimes G$ is homeomorphic to the orbit space of this action via induction. In addition, we give a strengthening of these results in the case where the crossed product is a groupoid algebra.

Keywords

crossed products algebraic group actions group actions

Cite

@article{arxiv.0908.1434,
  title  = {The Mackey Machine for Crossed Products by Regular Groupoids. II},
  author = {Geoff Goehle},
  journal= {arXiv preprint arXiv:0908.1434},
  year   = {2009}
}

Comments

Results have been extended to groupoids with potentially nonabelian stabilizers, 18 pages

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